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On the mathematical representation of nonlinearity

2008/07/07 by Emanuel Gluskin, Gluskin, Emanuel
Engineering · Physics and Astronomy · #Advanced Control Systems Optimization #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Control Systems and Identification #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · pdf · doi:10.48550/arxiv.0807.0966

openalex publication_date 2008/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The suggestion of writing, for some problems, nonlinear state equations not as dx/dt = F(x,u,t), but as dx/dt = [A(t,x)]x + [B(t,x)]u(t), which is more "constructive", is considered supported by arguments related to: the axiomatization of system theory, the classification of switched circuits as linear and nonlinear, the use of nonlinear sampling for measuring frequency without clock, the consideration of an ensemble of colliding particles in which the establishing of the chaotic movements is seen as a result of the same kind of nonlinearity as in electronic switching circuits, the modeling of a liquid medium as a "system" whose structure is directly influenced by the "input", and some other problems.

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